Question 1

A proton initially moves left to right along the x axis at a speed of 7.0 × 10³ m/s.It moves into an electric field,which points in the negative x direction,and travels a distance of 0.70 m before coming to rest.What acceleration magnitude does the proton experience?

Accepted Answer

The correct answer is B because the acceleration of the proton is given by the equation a = (v^2 - u^2) / 2s, where v is the final velocity, u is the initial velocity, and s is the distance traveled. In this case, v = 0 m/s, u = 7.0 × 10^3 m/s, and s = 0.70 m. Plugging these values into the equation, we get a = (0^2 - (7.0 × 10^3)^2) / 2(0.70) = 3.5 × 10^7 m/s^2.

Question 2

Two charges,+Q and −Q,are located two meters apart and there is a point along the line that is equidistant from the two charges as indicated.Which vector best represents the direction of the electric field at that point?

Accepted Answer

The answer of Two charges,+Q and −Q,are located two meters...

Question 3

An airplane is flying through a thundercloud at a height of 2 500 m.(This is a very dangerous thing to do because of updrafts,turbulence,and the possibility of electric discharge. )If there is a charge concentration of +42 C at height 4 000 m within the cloud and −42 C at height 500 m,what is the magnitude of the electric field E at the aircraft? (k_e = 8.99 × 10⁹ N·m²/C²)

Accepted Answer

The answer of An airplane is flying through a thundercloud...

Question 4

A proton moving at 3.0 × 10⁴ m/s is projected at an angle of 30° above a horizontal plane.If an electric field of 400 N/C is acting down,how long does it take the proton to return to the horizontal plane? (Hint: Ignore gravity.m_proton = 1.67 × 10−²⁷ kg,q_proton = 1.6 × 10−¹⁹ C)

Accepted Answer

The vertical component of velocity is affected by the electric field. Calculate the vertical acceleration using F = qE = ma, then use kinematic equations to find the time to return to the horizontal plane.

Question 5

Charges of 3.5 µC and −7.6 µC are placed at two corners of an equilateral triangle with sides of 0.1 m.At the third corner,what is the electric field magnitude created by these two charges? (k_e = 8.99 × 10⁹ N·m²/C²)

Accepted Answer

The electric field magnitude at the third corner due to each charge can be calculated using Coulomb's law formula for the electric field, $E = k \frac{|q|}{r^2}$, where $k = 8.99 \times 10^9 \, \text{N}\cdot\text{m}^2/\text{C}^2$, $q$ is the charge, and $r$ is the distance from the charge to the point of interest (0.1 m in this case). For the 3.5 µC charge: $E_1 = 8.99 \times 10^9 \times \frac{3.5 \times 10^{-6}}{(0.1)^2} = 3.1455 \times 10^6 \, \text{N/C}$.For the -7.6 µC charge: $E_2 = 8.99 \times 10^9 \times \frac{7.6 \times 10^{-6}}{(0.1)^2} = 6.7912 \times 10^6 \, \text{N/C}$.Since the triangle is equilateral, the angle between the directions of the electric fields due to each charge at the third corner is 120 degrees. The resultant electric field can be found using vector addition, where the components of the electric fields add up to give the total electric field. The magnitude of the resultant electric field $E$ can be calculated using the law of cosines or by recognizing the symmetry in the problem and using vector components:$$E = \sqrt{E_1^2 + E_2^2 + 2E_1E_2\cos(120^\circ)}$$Given $\cos(120^\circ) = -0.5$,$$E = \sqrt{(3.1455 \times 10^6)^2 + (6.7912 \times 10^6)^2 - (3.1455 \times 10^6)(6.7912 \times 10^6)}$$$$E \approx 5.9 \times 10^6 \, \text{N/C}$$Thus, the correct answer is D) 5.9E+6 N/C.

Question 6

In x-ray machines,electrons are subjected to electric fields as great as 6.0 × 10⁵ N/C.Find an electron's acceleration in this field.(m_e = 9.11 × 10−³¹ kg,e = 1.6 × 10−¹⁹ C)

Accepted Answer

The acceleration of an electron in an electric field is given by $a = \frac{F}{m}$, where $F = eE$ is the force on the electron, $e$ is the charge of the electron, $E$ is the electric field, and $m$ is the mass of the electron. Substituting the given values, $a = \frac{(1.6 \times 10^{-19} \, \text{C}) \times (6.0 \times 10^{15} \, \text{N/C})}{9.11 \times 10^{-31} \, \text{kg}} = 1.05 \times 10^{17} \, \text{m/s}^2$, which rounds to $1.1 \times 10^{17} \, \text{m/s}^2$.

Question 7

The average distance of the electron from the proton in the hydrogen atom is 0.65 × 10−¹⁰ m.What is the electric field from the proton's charge at the location of the electron? (k_e = 8.99 × 10⁹ N⋅m²/C²,e = 1.6 × 10−¹⁹ C)

Accepted Answer

The electric field $E$ from a point charge, like a proton, is given by $E = \frac{k|q|}{r^2}$, where $k = 8.99 \times 10^9 \, \text{N}\cdot\text{m}^2/\text{C}^2$, $q = 1.6 \times 10^{-19} \, \text{C}$ is the charge of the proton (or electron), and $r = 0.65 \times 10^{-10} \, \text{m}$ is the distance between the proton and the electron. Plugging these values into the formula gives $E = \frac{8.99 \times 10^9 \times 1.6 \times 10^{-19}}{(0.65 \times 10^{-10})^2} \, \text{N/C}$, which calculates to approximately $3.4 \times 10^{11} \, \text{N/C}$.

Question 8

A proton initially moves left to right long the x axis at a speed of 9.0 × 10³ m/s.It moves into an electric field,which points in the negative x direction,and travels a distance of 0.8 m before coming to rest.If the proton's mass and charge are 1.67 × 10−²⁷ kg and 1.60 × 10−¹⁹ C respectively,what is the magnitude of the electric field?

Accepted Answer

The answer of A proton initially moves left to right...

Question 9

Two point charges are placed along a horizontal axis with the following values and positions: +3.8 µC at x = 0 cm and −7.6 µC at x = 20 cm.At what point along the x axis is the electric field zero?​

Accepted Answer

The electric field is zero at a point where the magnitudes of the electric fields due to each charge are equal. Since the negative charge is larger in magnitude, the point where the electric field is zero must be to the left of the positive charge (x = 0 cm). By setting up the equation for the electric fields due to each charge being equal and solving for the position, we find that this point is to the left of the positive charge, resulting in a negative x-value, which matches option D, -48 cm.

Question 10

Charges q,q,and -q are placed on the x-axis at x = 0,x = 4 m,and x = 6 m,respectively.At which of the following points does the electric field have the greatest magnitude?​

Accepted Answer

At x = 5 m, the point is equidistant from the charges q and -q, leading to a superposition of electric fields that enhances the magnitude at this point compared to the others.

Question 11

A ring of charge of radius r₀ lies in the x-y plane with its center at the origin.The charge counterclockwise from θ = 0º to θ = 180º is uniformly distributed with the total charge equaling Q.The charge counterclockwise from θ = 180º to θ = 360º is uniformly distributed with the total charge for this half of the ring equaling -Q.What is the direction of the electric field on the z-axis at the position (x,y,z)= (0,0,r₀)?

Accepted Answer

The answer of A ring of charge of radius r₀...

Question 12

Two point charges,separated by 1.7 cm,have charge values of +2.0 and −4.0 µC,respectively.Suppose we determine that 50 field lines radiate out from the +2.0-µC charge.If so,what might be inferred about the −4.0-μC charge with respect to field lines?​

Accepted Answer

Electric field lines originate from positive charges and terminate on negative charges. Since the negative charge is twice the magnitude of the positive charge, it will have twice the number of field lines terminating on it compared to those originating from the positive charge. Therefore, if 50 field lines radiate out from the +2.0-µC charge, 100 field lines will terminate on the -4.0-µC charge, indicating 100 field lines radiate in towards the negative charge.

Question 13

An electron with a speed of 2.0 × 10⁶ m/s moves into a uniform electric field of 550 N/C that is parallel to the electron's motion.How long does it take to bring the electron to rest? (me = 9.11 × 10−³¹ kg,e = 1.6 × 10−¹⁹ C)

Accepted Answer

The time it takes to bring the electron to rest can be calculated using the equation $t = \frac{v}{a}$, where $v$ is the initial velocity of the electron and $a$ is the acceleration caused by the electric field. The force on the electron due to the electric field is $F = eE$, where $e$ is the charge of the electron and $E$ is the electric field strength. The acceleration $a$ is then $F/m_e = eE/m_e$. Substituting the given values: $a = (1.6 \times 10^{-19} \, \text{C}) \times (550 \, \text{N/C}) / (9.11 \times 10^{-31} \, \text{kg})$, and then calculating $t = v/a$ with $v = 2.0 \times 10^6 \, \text{m/s}$, we find the time to bring the electron to rest.

Question 14

The electric field in a cathode ray tube is supposed to accelerate electrons from 0 to 3.2 × 10⁷ m/s in a distance of 2.00 cm.What electric field is required? (m_e = 9.11 × 10−³¹ kg and e = 1.60 × 10−¹⁹ C)

Accepted Answer

The answer of The electric field in a cathode ray...

Question 15

The number of electric field lines passing through a unit cross-sectional area is indicative of

Accepted Answer

The number of electric field lines passing through a unit cross-sectional area is indicative of the field strength. The greater the number of field lines, the stronger the electric field. The direction of the field can be determined by observing the direction of the field lines, but it is not directly related to the number of field lines passing through a unit cross-sectional area. Charge density and charge motion are not directly related to the number of field lines passing through a unit cross-sectional area.

Question 16

Charge A has 10 electric field lines coming out,Charge B has 20 lines coming out,and Charge C has 30 lines coming in.Which pair of these charges will have the largest force between them if placed one cm apart?

Accepted Answer

The force between two charges is proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. Therefore, the force between Charges A and B will be (10 x 20)/(1^2) = 200, the force between Charges B and C will be (20 x 30)/(1^2) = 600, and the force between Charges C and A will be (30 x 10)/(1^2) = 300. Therefore, the greatest force will be between Charges B and C.

Question 17

Three equal positive charges are placed on the x-axis,one at the origin,one at x = 4 m,and the third at x = 7 m.Of the following points,which has the greatest magnitude electric field?​

Accepted Answer

The answer of Three equal positive charges are placed on...

Question 18

Electrons in a particle beam each have a kinetic energy of 4.0 × 10−¹⁷ J.What is the magnitude of the electric field that will stop these electrons in a distance of 0.3 m? (e = 1.6 × 10−¹⁹ C)

Accepted Answer

The work done by an electric field on a charge is given by the equation:

W = qΔV

where q is the charge, ΔV is the potential difference, and W is the work done.

Since the electrons are being stopped, their final kinetic energy is zero. Therefore, the work done by the electric field is equal to the initial kinetic energy of the electrons:

W = ΔK = 4.0 × 10^-11 J

The potential difference ΔV is related to the electric field E and the distance d:

ΔV = Ed

Therefore,

E = ΔV / d

Substituting the given values, we get:

E = (4.0 × 10^-11 J) / (1.6 × 10^-19 C) / (0.3 m)

E = 8.3 × 10^2 N/C

Therefore, the answer is C.

Question 19

A charge of +2 C is at the origin.When charge Q is placed at 2 m along the positive x axis,the electric field at 2 m along the negative x axis becomes zero.What is the value of Q?

Accepted Answer

The answer of A charge of +2 C is at...

Question 20

Q₁ has 50 electric field lines radiating outward and Q₂ has 250 field lines converging inward.What is the ratio Q₁/Q₂?

Accepted Answer

The number of electric field lines is proportional to the charge. Since Q1 has 50 lines radiating outward (positive charge) and Q2 has 250 lines converging inward (negative charge), the ratio Q1/Q2 is 50/-250 = -1/5.

Quiz 15: Electric Forces and Fields

A proton initially moves left to right along the x axis at a speed of 7.0 × 103 m/s.It moves into an electric field,which points in the negative x direction,and travels a distance of 0.70 m before coming to rest.What acceleration magnitude does the proton experience?​

Two charges,+Q and −Q,are located two meters apart and there is a point along the line that is equidistant from the two charges as indicated.Which vector best represents the direction of the electric field at that point?

A proton moving at 3.0 × 104 m/s is projected at an angle of 30° above a horizontal plane.If an electric field of 400 N/C is acting down,how long does it take the proton to return to the horizontal plane? (Hint: Ignore gravity.mproton = 1.67 × 10−27 kg,qproton = 1.6 × 10−19 C)

Charges of 3.5 µC and −7.6 µC are placed at two corners of an equilateral triangle with sides of 0.1 m.At the third corner,what is the electric field magnitude created by these two charges? (ke = 8.99 × 109 N·m2/C2) ​

In x-ray machines,electrons are subjected to electric fields as great as 6.0 × 105 N/C.Find an electron's acceleration in this field.(me = 9.11 × 10−31 kg,e = 1.6 × 10−19 C)

The average distance of the electron from the proton in the hydrogen atom is 0.65 × 10−10 m.What is the electric field from the proton's charge at the location of the electron? (ke = 8.99 × 109 N⋅m2/C2,e = 1.6 × 10−19 C) ​

Two point charges are placed along a horizontal axis with the following values and positions: +3.8 µC at x = 0 cm and −7.6 µC at x = 20 cm.At what point along the x axis is the electric field zero?​

Charges q,q,and -q are placed on the x-axis at x = 0,x = 4 m,and x = 6 m,respectively.At which of the following points does the electric field have the greatest magnitude?​

Two point charges,separated by 1.7 cm,have charge values of +2.0 and −4.0 µC,respectively.Suppose we determine that 50 field lines radiate out from the +2.0-µC charge.If so,what might be inferred about the −4.0-μC charge with respect to field lines?​

An electron with a speed of 2.0 × 106 m/s moves into a uniform electric field of 550 N/C that is parallel to the electron's motion.How long does it take to bring the electron to rest? (me = 9.11 × 10−31 kg,e = 1.6 × 10−19 C)

The electric field in a cathode ray tube is supposed to accelerate electrons from 0 to 3.2 × 107 m/s in a distance of 2.00 cm.What electric field is required? (me = 9.11 × 10−31 kg and e = 1.60 × 10−19 C) ​

The number of electric field lines passing through a unit cross-sectional area is indicative of

Charge A has 10 electric field lines coming out,Charge B has 20 lines coming out,and Charge C has 30 lines coming in.Which pair of these charges will have the largest force between them if placed one cm apart?

Three equal positive charges are placed on the x-axis,one at the origin,one at x = 4 m,and the third at x = 7 m.Of the following points,which has the greatest magnitude electric field?​

Electrons in a particle beam each have a kinetic energy of 4.0 × 10−17 J.What is the magnitude of the electric field that will stop these electrons in a distance of 0.3 m? (e = 1.6 × 10−19 C)

A charge of +2 C is at the origin.When charge Q is placed at 2 m along the positive x axis,the electric field at 2 m along the negative x axis becomes zero.What is the value of Q?

Q1 has 50 electric field lines radiating outward and Q2 has 250 field lines converging inward.What is the ratio Q1/Q2?​

A proton initially moves left to right along the x axis at a speed of 7.0 × 10³ m/s.It moves into an electric field,which points in the negative x direction,and travels a distance of 0.70 m before coming to rest.What acceleration magnitude does the proton experience?

A proton moving at 3.0 × 10⁴ m/s is projected at an angle of 30° above a horizontal plane.If an electric field of 400 N/C is acting down,how long does it take the proton to return to the horizontal plane? (Hint: Ignore gravity.m_proton = 1.67 × 10−²⁷ kg,q_proton = 1.6 × 10−¹⁹ C)

Charges of 3.5 µC and −7.6 µC are placed at two corners of an equilateral triangle with sides of 0.1 m.At the third corner,what is the electric field magnitude created by these two charges? (k_e = 8.99 × 10⁹ N·m²/C²)

In x-ray machines,electrons are subjected to electric fields as great as 6.0 × 10⁵ N/C.Find an electron's acceleration in this field.(m_e = 9.11 × 10−³¹ kg,e = 1.6 × 10−¹⁹ C)

The average distance of the electron from the proton in the hydrogen atom is 0.65 × 10−¹⁰ m.What is the electric field from the proton's charge at the location of the electron? (k_e = 8.99 × 10⁹ N⋅m²/C²,e = 1.6 × 10−¹⁹ C)

Two point charges are placed along a horizontal axis with the following values and positions: +3.8 µC at x = 0 cm and −7.6 µC at x = 20 cm.At what point along the x axis is the electric field zero?

Charges q,q,and -q are placed on the x-axis at x = 0,x = 4 m,and x = 6 m,respectively.At which of the following points does the electric field have the greatest magnitude?

Two point charges,separated by 1.7 cm,have charge values of +2.0 and −4.0 µC,respectively.Suppose we determine that 50 field lines radiate out from the +2.0-µC charge.If so,what might be inferred about the −4.0-μC charge with respect to field lines?

An electron with a speed of 2.0 × 10⁶ m/s moves into a uniform electric field of 550 N/C that is parallel to the electron's motion.How long does it take to bring the electron to rest? (me = 9.11 × 10−³¹ kg,e = 1.6 × 10−¹⁹ C)

The electric field in a cathode ray tube is supposed to accelerate electrons from 0 to 3.2 × 10⁷ m/s in a distance of 2.00 cm.What electric field is required? (m_e = 9.11 × 10−³¹ kg and e = 1.60 × 10−¹⁹ C)

Three equal positive charges are placed on the x-axis,one at the origin,one at x = 4 m,and the third at x = 7 m.Of the following points,which has the greatest magnitude electric field?

Electrons in a particle beam each have a kinetic energy of 4.0 × 10−¹⁷ J.What is the magnitude of the electric field that will stop these electrons in a distance of 0.3 m? (e = 1.6 × 10−¹⁹ C)

Q₁ has 50 electric field lines radiating outward and Q₂ has 250 field lines converging inward.What is the ratio Q₁/Q₂?